Junior one mathematics knowledge points

First unit position

1, you can determine the position of the method under certain circumstances, such as the position of an object.

2. Use a "number pair" to indicate the position, in which the number on the corresponding column appears first, and the number on the line appears last, and is recorded as (x, y).

3. "Number pair" indicates position, and there are (x, 0) and (0, y) which are easy to make mistakes.

4, know the direction, up north, down south, left west, right east, two things in each other's direction.

Unit 2 Fractional Multiplication

I. Fraction multiplied by integer

1, meaning: it means the addition of several identical scores.

2. Calculation method: (1), denominator unchanged, numerator multiplied by integer.

(2), denominator and integer can be reduced, the first thing to reduce points.

Second, multiply the score by the score.

1, meaning: it is a fraction of the score.

2. Calculation method: (1), numerator multiplied by numerator, denominator multiplied by denominator. .

(2) If both numerator and denominator have lower offer scores, then calculate.

Third, the application of operation method.

1 and integer multiplication are also applicable to fractional multiplication.

2. Use the algorithm for simple calculation.

Fourth, the countdown.

Two numbers whose product is 1 are reciprocal.

2. Solution: Reverse the position of numerator and denominator.

3. The reciprocal of 1 is1itself, and 0 has no reciprocal.

Verbs (short for verb) solve problems.

1, find the fraction of a number. Formula: standard quantity × fraction

2. Find the fraction of a number. Formula: standard quantity × (1 fraction)

Standard soil standard quantity × fraction

3. Find the fraction of one number to another. Formula: What score?

4. Analyze the quantitative relationship of fractional multiplication application problems by drawing line segments.

Unit 3 Fractional Division

I. Types

1, when the fraction is divided by an integer, it means that the fraction is evenly divided into integer parts.

2. Divide the score by the score and indicate how many D/Cs there are in B/A. ..

3. Integer divided by fraction indicates how many C/Ds there are in A. ..

Second, the calculation method: dividing by a number is equal to multiplying the reciprocal of this number (except 0).

Third, the significance of fractional division is the same as integer division, which is the inverse operation of multiplication.

Fourth, fractional mixed operation sequence, the algorithm is simple.

Verbs (short for verb) solve problems.

1, a number is a fraction of b number. Formula: a/B.

2. what fraction of b is equal to a? Formula: number A = number B × fraction.

Number b = number a/ fraction.

3. How much is A more (or less) than B?

Formula: number A = number B× (1soil fraction)

Number A = number b, number B × fraction.

Standard quantity: the standard quantity follows the word "than".

4. If the length of a rectangle is several times the width, it is the aspect ratio: length/width.

If the width of a rectangle is a fraction of its length, then it is the aspect ratio: length/width.

VI. Meaning of ratio: Divided by two numbers, it is also called the ratio of two numbers, and the result of the symbol ":"is called ratio.

1. In A: B, A is the first term of the ratio and B is the last term of the ratio.

2. The relationship between ratio, division and score. a:b=a÷b=a/b .

3. The unit names of the two proportions should be unified. The ratio is a number and there is no unit.

4. Basic properties of the ratio A: B = AM: BM

a:b = a \u m:b \u m

5. The ratio becomes the simplest integer ratio:

(1) has a fraction, and the first term and the last term are multiplied by the least common multiple of the denominator.

(2) No score, the first and last items are divided by the greatest common divisor.

(3) There are decimals, which can be converted into integers or fractions first.

6. The total number of problems × points/total points = required amount.

Unit 4 circle

First, the understanding of the circle, surrounded by curves, is beautiful in appearance and easy to roll.

1, the center of the circle, represented by O.

2, radius, the line segment connecting the center of the circle and any point on the circle is called radius, which is expressed by R.

3, diameter, the line segment on the circle passing through the center and both ends is called diameter, which is expressed by D.

4. The relationship between radius and diameter.

5. Axisymmetric figure and axis of symmetry. A circle has countless axes of symmetry, which is the straight line where the diameter lies.

Second, the circumference of the circle.

1, pi is the ratio of circumference to diameter, and it is an infinite acyclic decimal.

2. Formula: c = π d or c = 2π r.

3. Find the radius and diameter from the circumference of a known circle.

Third, the area of the circle.

1, formula s = π R2.

2. Given the radius, diameter or circumference of a circle, the area of the circle can be calculated separately.

3. Annular area formula S = π R2-π R2

4. Sector, arc and central angle.

5. When the perimeter is fixed, the area of the circle is the largest.

In the case of a certain area, the circumference of a circle is the shortest.

6. Determine the position of the starting line.

Unit 5 Percentage

1, the percentage written. Percent sign "%"

2. Meaning of percentage: It means that one number is the percentage of another number.

3. The difference between percentage and fraction: a fraction can represent a specific number or the relationship between two numbers. Percent means that one number is the percentage of another number, which only means the relationship between the two numbers, not the specific number, and you can't write the company name. The other part of molecules can be decimals and numbers greater than one hundred.

4. Conversion between percentages, fractions and decimals.

Decimal percentage: remove the percent sign and move the decimal point to the left by two places;

Decimal to percentage: move the decimal point two places to the right and add hundreds of semicolons;

Convert percentage into fraction: fraction with denominator of 100 can be converted into fractional quotation;

Convert Fractions into Percentages: Convert Fractions into Decimals and then into Percentages.

Step 5 solve the problem

(1), standard rate and germination rate. What is the percentage of A to B? )

The compliance rate = the number of people meeting the standards/the total number of people × 100%.

Germination rate = germination number/total number of seeds × 100%

(2) What percentage of A is less (or more) than B? Determine the unit "1".

(3) What percentage has A increased? How much has it increased?

6. Discount means a few tenths, that is, dozens of percent.

The discount problem is a question of what percentage of a number is.

7. Pay taxes.

(1), according to the provisions of the tax laws of various countries, according to a certain proportion, giving a part of the collective or individual income to the state is called tax.

② The tax paid is called taxable. Paying taxes according to a certain tax rate is called tax rate.

③ Tax rate = tax payable/income × 100%.

Taxable amount = tax rate × various incomes.

8. Interest rate.

(1), the benefits of deposit.

② Interest = principal × interest rate × time

③ Extraction = principal+interest-interest tax (principal+after-tax interest).

Unit 6 Statistics

First, the fan list

1, which can reflect the relationship between partial quantity and total quantity.

2. Use the whole circle to represent the total amount, and use each sector to represent the percentage of each part in the total amount.

3. Use the fan-shaped statistical chart for calculation and analysis.